Complex Numbers Flashcard

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

What is the imaginary unit 'i'?

Back

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is the complex conjugate of a complex number?

Back

The complex conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Front

What is the formula for dividing complex numbers?

Back

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It is used when multiplying complex numbers.

Front

What is the Commutative Property?

Back

The Commutative Property states that a + b = b + a and ab = ba. It applies to addition and multiplication of complex numbers.